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## PowerPoint Slideshow about 'Introduction to Programming' - Pat_Xavi

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Introduction

- An introduction to programming concepts
- Simple calculator
- Declarative variables
- Functions
- Structured data (example: lists)
- Functions over lists
- Correctness and complexity
- Lazy functions
- Concurrency and dataflow
- State, objects, and classes
- Nondeterminism and atomicity

S. Haridi and P. Van Roy

Variables

- Variables are short-cuts for values, they cannot be assigned more than once

declare

V = 9999*9999

{Browse V*V}

- Variable identifiers: is what you type
- Store variable: is part of the memory system
- The declare statement creates a store variable and assigns its memory address to the identifier ’V’ in the environment

S. Haridi and P. Van Roy

Functions

- Compute the factorial function:
- Start with the mathematical definition

declare

fun {Fact N}

if N==0 then 1 else N*{Fact N-1} end

end

- Fact is declared in the environment
- Try large factorial {Browse {Fact 100}}

S. Haridi and P. Van Roy

Composing functions

- Combinations of r items taken from n.
- The number of subsets of size r taken from a set of size n

Comb

declare

fun {Comb N R}

{Fact N} div ({Fact R}*{Fact N-R})

end

Fact

Fact

Fact

- Example of functional abstraction

S. Haridi and P. Van Roy

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Structured data (lists)- Calculate Pascal triangle
- Write a function that calculates the nth row as one structured value
- A list is a sequence of elements:

[1 4 6 4 1]

- The empty list is written nil
- Lists are created by means of ”|” (cons)

declare

H=1

T = [2 3 4 5]

{Browse H|T} % This will show [1 2 3 4 5]

S. Haridi and P. Van Roy

Lists (2)

- Taking lists apart (selecting components)
- A cons has two components a head, and tail

declare L = [5 6 7 8]

L.1 gives 5

L.2 give [6 7 8]

‘|’

6

‘|’

‘|’

7

8

nil

S. Haridi and P. Van Roy

Pattern matching

- Another way to take a list apart is by use of pattern matching with a case instruction

case L of H|T then {Browse H} {Browse T} end

S. Haridi and P. Van Roy

Functions over lists

- Compute the function {Pascal N}
- Takes an integer N, and returns the Nth row of a Pascal triangle as a list
- For row 1, the result is [1]
- For row N, shift to left row N-1 and shift to the right row N-1
- Align and add the shifted rows element-wise to get row N

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(0)

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(0)

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Shift right

[0 1 3 3 1]

[1 3 3 1 0]

Shift left

S. Haridi and P. Van Roy

Functions over lists (2)

Pascal N

declare

fun {Pascal N}

if N==1 then [1]

else

{AddList

{ShiftLeft {Pascal N-1}}

{ShiftRight {Pascal N-1}}}

end

end

Pascal N-1

Pascal N-1

ShiftLeft

ShiftRight

AddList

S. Haridi and P. Van Roy

Functions over lists (3)

fun {ShiftLeft L}

case L of H|T then

H|{ShiftLeft T}

else [0]

end

end

fun {ShiftRight L} 0|L end

fun {AddList L1 L2}

case L1 of H1|T1 then

case L2 of H2|T2 then

H1+H2|{AddList T1 T2}

end

else nil end

end

S. Haridi and P. Van Roy

Top-down program development

- Understand how to solve the problem by hand
- Try to solve the task by decomposing it to simpler tasks
- Devise the main function (main task) in terms of suitable auxiliary functions (subtasks) that simplifies the solution (ShiftLeft, ShiftRight and AddList)
- Complete the solution by writing the auxiliary functions

S. Haridi and P. Van Roy

Is your program correct?

- ”A program is correct when it does what we would like it to do”
- In general we need to reason about the program:
- Semantics for the language: a precise model of the operations of the programming language
- Program specification: a definition of the output in terms of the input (usually a mathematical function or relation)
- Use mathematical techniques to reason about the program, using programming language semantics

S. Haridi and P. Van Roy

Mathematical induction

- Select one or more input to the function
- Show the program is correct for the simple cases (base case)
- Show that if the program is correct for a given case, it is then correct for the next case.
- For integers base case is either 0 or 1, and for any integer n the next case is n+1
- For lists the base case is nil, or a list with one or few elements, and for any list T the next case H|T

S. Haridi and P. Van Roy

Correctness of factorial

fun {Fact N}

if N==0 then 1 else N*{Fact N-1} end

end

- Base Case: {Fact 0} returns 1
- (N>1),N*{Fact N-1}assume {Fact N-1} is correct, from the spec we see the {Fact N} is N*{Fact N-1}
- More techniques to come !

S. Haridi and P. Van Roy

Complexity

- Pascal runs very slow, try {Pascal 24}
- {Pascal 20} calls: {Pascal 19} twice, {Pascal 18} four times, {Pascal 17} eight times, ..., {Pascal 1} 219 times
- Execution time of a program up to a constant factor is called program’s time complexity.
- Time complexity of {Pascal N} is proportional to 2N (exponential)
- Programs with exponential time complexity are impractical

declare

fun {Pascal N}

if N==1 then [1]

else

{AddList

{ShiftLeft {Pascal N-1}}

{ShiftRight {Pascal N-1}}}

end

end

S. Haridi and P. Van Roy

Faster Pascal

- Introduce a local variable L
- Compute {FastPascal N-1} only once
- Try with 30 rows.
- FastPascal is called N times, each time a list on the average of size N/2 is processed
- The time complexity is proportional to N2 (polynomial)
- Low order polynomial programs are practical.

fun {FastPascal N}

if N==1 then [1]

else

local L in

L={FastPascal N-1}

{AddList {ShiftLeft L} {ShiftRight L}}

end

end

end

S. Haridi and P. Van Roy

Lazy evaluation

- The functions written so far are evaluated eagerly (as soon as they are called)
- Another way is lazy evaluation where a computation is done only when the results is needed

- Calculates the infinite list:0 | 1 | 2 | 3 | ...

declare

funlazy {Ints N}

N|{Ints N+1}

end

S. Haridi and P. Van Roy

Lazy evaluation (2)

- Write a function that computes as many rows of Pascal’s triangle as needed
- We do not know how many beforehand
- A function is lazy if it is evaluated only when its result is needed
- The function PascalList is evaluated when needed

funlazy {PascalList Row}

Row | {PascalList

{AddList

{ShiftLeft Row}

{ShiftRight Row}}}

end

S. Haridi and P. Van Roy

Lazy evaluation (3)

declare

L = {PascalList [1]}

{Browse L}

{Browse L.1}

{Browse L.2.1}

- Lazy evaluation will avoid redoing work if you decide first you need the 10th row and later the 11th row
- The function continues where it left off

L<Future>

[1]

[1 1]

S. Haridi and P. Van Roy

Higher-order programming

- Assume we want to write another Pascal function which instead of adding numbers performs exclusive-or on them
- It calculates for each number whether it is odd or even (parity)
- Either write a new function each time we need a new operation, or write one generic function that takes an operation (another function) as argument
- The ability to pass functions as argument, or return a function as result is called higher-order programming
- Higher-order programming is an aid to build generic abstractions

S. Haridi and P. Van Roy

Variations of Pascal

- Compute the parity Pascal triangle

fun {Xor X Y} if X==Y then 0 else 1 endend

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S. Haridi and P. Van Roy

Higher-order programming

fun {Add N1 N2} N1+N2 end

fun {Xor N1 N2}

if N1==N2 then 0 else 1 end

end

fun {Pascal N} {GenericPascal Add N} end

fun {ParityPascal N}

{GenericPascal Xor N}

end

fun {GenericPascal Op N}

if N==1 then [1]

else L in L = {GenericPascal Op N-1}

{OpList Op {ShiftLeft L} {ShiftRight L}}

end

end

fun {OpList Op L1 L2}

case L1 of H1|T1 then

case L2 of H2|T2 then

{Op H1 H2}|{OpList Op T1 T2}

end

end

else nil end

end

S. Haridi and P. Van Roy

Concurrency

- How to do several things at once
- Concurrency: running several activities each running at its own pace
- A thread is an executing sequential program
- A program can have multiple threads by using the thread instruction
- {Browse 99*99}can immediately respond while Pascal is computing

thread

P in

P = {Pascal 21}

{Browse P}

end

{Browse 99*99}

S. Haridi and P. Van Roy

Dataflow

- What happens when multiple threads try to communicate?
- A simple way is to make communicating threads synchronize on the availability of data (data-driven execution)
- If an operation tries to use a variable that is not yet bound it will wait
- The variable is called a dataflow variable

X

Y

Z

U

*

*

+

S. Haridi and P. Van Roy

Dataflow (II)

- Two important properties of dataflow
- Calculations work correctly independent of how they are partitioned between threads (concurrent activities)
- Calculations are patient, they do not signal error; they wait for data availability
- The dataflow property of variables makes sense when programs are composed of multiple threads

declare X

thread

{Delay 5000} X=99

end

{Browse ‘Start’} {Browse X*X}

declare X

thread

{Browse ‘Start’} {Browse X*X}

end

{Delay 5000} X=99

S. Haridi and P. Van Roy

State

- How to make a function learn from its past?
- We would like to add memory to a function to remember past results
- Adding memory as well as concurrency is an essential aspect of modeling the real world
- Consider {FastPascal N}: we would like it to remember the previous rows it calculated in order to avoid recalculating them
- We need a concept (memory cell) to store, change and retrieve a value
- The simplest concept is a (memory) cell which is a container of a value
- One can create a cell, assign a value to a cell, and access the current value of the cell
- Cells are not variables

declare

C = {NewCell 0}

{Assign C {Access C}+1}

{Browse {Access C}}

S. Haridi and P. Van Roy

Example

- Add memory to Pascal to remember how many times it is called
- The memory (state) is global here
- Memory that is local to a function is called encapsulated state

declare

C = {NewCell 0}

fun {FastPascal N}

{Assign C {Access C}+1}

{GenericPascal Add N}

end

S. Haridi and P. Van Roy

Objects

- Functions with internal memory are called objects
- The cell is invisible outside of the definition

declare

local C in

C = {NewCell 0}

fun {Bump}

{Assign C {Access C}+1}

{Access C}

end

end

declare

fun {FastPascal N}

{Browse {Bump}}

{GenericPascal Add N}

end

S. Haridi and P. Van Roy

Classes

- A class is a ’factory’ of objects where each object has its own internal state
- Let us create many independent counter objects with the same behavior

fun {NewCounter}

local C Bump in

C = {NewCell 0}

fun {Bump}

{Assign C {Access C}+1}

{Access C}

end

Bump

end

end

S. Haridi and P. Van Roy

Classes (2)

- Here is a class with two operations: Bump and Read

fun {NewCounter}

local C Bump in

C = {NewCell 0}

fun {Bump}

{Assign C {Access C}+1}

{Access C}

end

fun {Read}

{Access C}

end

[Bump Read]

end

end

S. Haridi and P. Van Roy

Object-oriented programming

- In object-oriented programming the idea of objects and classes is pushed farther
- Classes keep the basic properties of:
- State encapsulation
- Object factories
- Classes are extended with more sophisticated properties:
- They have multiple operations (called methods)
- They can be defined by taking another class and extending it slightly (inheritance)

S. Haridi and P. Van Roy

Nondeterminism

- What happens if a program has both concurrency and state together?
- This is very tricky
- The same program can give different results from one execution to the next
- This variability is called nondeterminism
- Internal nondeterminism is not a problem if it is not observable from outside

S. Haridi and P. Van Roy

Nondeterminism (2)

declare

C = {NewCell 0}

thread {Assign C 1} end

thread {Assign C 2} end

C = {NewCell 0}

cell C contains 0

t0

{Assign C 1}

cell C contains 1

t1

{Assign C 2}

cell C contains 2 (final value)

t2

time

S. Haridi and P. Van Roy

Nondeterminism (3)

declare

C = {NewCell 0}

thread {Assign C 1} end

thread {Assign C 2} end

C = {NewCell 0}

cell C contains 0

t0

{Assign C 2}

cell C contains 2

t1

{Assign C 1}

cell C contains 1 (final value)

t2

time

S. Haridi and P. Van Roy

Nondeterminism (4)

declare

C = {NewCell 0}

thread I in

I = {Access C}

{Assign C I+1}

end

thread J in

J = {Access C}

{Assign C J+1}

end

- What are the possible results?
- Both threads increment the cell C by 1
- Expected final result of C is 2
- Is that all?

S. Haridi and P. Van Roy

Nondeterminism (5)

- Another possible final result is the cell C containing the value 1

C = {NewCell 0}

t0

t1

I = {Access C}

I equal 0

declare

C = {NewCell 0}

thread I in

I = {Access C}

{Assign C I+1}

end

thread J in

J = {Access C}

{Assign C J+1}

end

t2

J = {Access C}

J equal 0

t3

{Assign C J+1}

C contains 1

t4

{Assign C I+1}

C contains 1

time

S. Haridi and P. Van Roy

Lessons learned

- Combining concurrency and state is tricky
- Complex programs have many possible interleavings
- Programming is a question of mastering the interleavings
- Famous bugs in the history of computer technology are due to designers overlooking an interleaving (e.g., the Therac-25 radiation therapy machine giving doses 1000’s of times too high, resulting in death or injury)
- If possible try to avoid concurrency and state together
- Encapsulate state and communicate between threads using dataflow
- Try to master interleavings by using atomic operations

S. Haridi and P. Van Roy

Atomicity

- How can we master the interleavings?
- One idea is to reduce the number of interleavings by programming with coarse-grained atomic operations
- An operation is atomic if it is performed as a whole or nothing
- No intermediate (partial) results can be observed by any other concurrent activity
- In simple cases we can use a lock to ensure atomicity of a sequence of operations
- For this we need a new entity (a lock)

S. Haridi and P. Van Roy

Atomicity (2)

declare

L = {NewLock}

lock L then

sequence of ops 1

end

lock L then

sequence of ops 2

end

Thread 1

Thread 2

S. Haridi and P. Van Roy

The program

declare

C = {NewCell 0}

L = {NewLock}

thread

lock L then I in

I = {Access C}

{Assign C I+1}

end

end

thread

lock L then J in

J = {Access C}

{Assign C J+1}

end

end

The final result of C is

always 2

S. Haridi and P. Van Roy

Additional exercises

- Write the memorizing Pascal function using the store abstraction (available at http://www.sics.se/~seif/DatalogiII/Examples/Store.oz)
- Reason about the correctness of AddList and ShiftLeft using induction

S. Haridi and P. Van Roy

Memoizing FastPascal

- {FastPascal N} New Version
- Make a store S available to FastPascal
- Let K be the number of the rows stored in S (i.e. max row is the Kth row)
- if N is less or equal K retrieve the Nth row from S
- Otherwise, compute the rows numbered K+1 to N, and store them in S
- Return the Nth row from S
- Viewed from outside (as a black box), this version behaves like the earlier one but faster

declare

S = {NewStore}

{Put S 2 [1 1]}

{Browse {Get S 2}}

{Browse {Size S}}

S. Haridi and P. Van Roy

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